Amazon said the decision to award a major deal to Microsoft was due to unfair political interference.
Amazon has filed an intention to appeal the US Department of Defense's decision to give a major contract to Microsoft.
Amazon had been considered the favourite to win the deal, worth $10bn over the next 10 years.
The company, which already provides cloud computing to the US Central Intelligence Agency, said the decision was made due to political pressure.
In July, President Donald Trump threatened to intervene after what he described as "tremendous complaints".
Mr Trump had previously attacked Amazon chief executive Jeff Bezos, owner of the Washington Post, which has been critical of his presidency.
The Pentagon subsequently delayed its decision to award the contract until 25 October, when it was announced the work would be given to Microsoft.
Defence Secretary Mark Esper said the competition was fair.
"I am confident it was conducted freely and fairly without any type of outside influence," he told reporters in the South Korean capital Seoul.
The Joint Enterprise Defense Infrastructure project - known as JEDI - is designed to modernise the antiquated data and communication systems within the US military. The contract is considered to be particularly lucrative if other government departments follow the Defense Department's lead when upgrading their own systems.
An Amazon spokesperson told the BBC: "Amazon Web Services is uniquely experienced and qualified to provide the critical technology the US military needs, and remains committed to supporting the DoD's modernisation efforts.
"We also believe it's critical for our country that the government and its elected leaders administer procurements objectively and in a manner that is free from political influence.
"Numerous aspects of the JEDI evaluation process contained clear deficiencies, errors and unmistakable bias - and it's important that these matters be examined and rectified."
The BBC understands Amazon submitted its intention to protest against the decision to the Court of Federal Claims last Friday. The formal appeal itself will be filed at a later stage.
Microsoft did not respond to requests for comment.
Four companies had initially been in the running for the deal when the process was launched two years ago. IBM was eliminated, as was Oracle - which lodged an unsuccessful legal challenge alleging conflict of interest stemming from Amazon's hiring of two former Defense Department employees. Both were said to have been involved in the JEDI selection process. BBC